Quantum phase transitions in coupled two-level atoms in a single-mode cavity

The dipole-coupled two-level atoms (qubits) in a single-mode resonant cavity are studied by extended bosonic coherent states. The numerical solution is presented. The first-order quantum phase transitions may occur in finite systems, in contrast to the original Dicke model. This system also exhibits a second-order quantum phase transition from the normal to the superradiant phase, as in the original Dicke model. Finite-size scaling for several observables---such as average fidelity susceptibility, order parameter, and concurrence---is performed for different interatomic interactions. The scaling exponents obtained suggest that interatomic interactions do not change the universality class.